
def a__       (			A_,	A_,	A_,	A_   ):






  '''simple docstring'''





  global f  # a global dp table for knapsack
  if f[i][j] < 0:
    if j < wt[i - 1]:
      __magic_name__								=			mf_knapsack(i - 1,	A_,	A_,	A_   )
    else:
      __magic_name__								=			max(
          mf_knapsack(i - 1,	A_,	A_,	A_   ),	mf_knapsack(i - 1,	A_,	A_,	j - wt[i - 1]   ) + val[i - 1],	)
    __magic_name__								=			val
  return f[i][j]

def a__       (			A_,	A_,	A_,	A_   ):






  '''simple docstring'''





  __magic_name__								=			[[0] * (w + 1) for _ in range(n + 1   )]

  for i in range(1,	n + 1   ):
    for w_ in range(1,	w + 1   ):
      if wt[i - 1] <= w_:
        __magic_name__								=			max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]],	dp[i - 1][w_]   )
      else:
        __magic_name__								=			dp[i - 1][w_]

  return dp[n][w_], dp

def a__       (			A_,	A_,	A_   ):






  '''simple docstring'''





  if not (isinstance(A_,	(list, tuple)   ) and isinstance(A_,	(list, tuple)   )):
    raise ValueError(
        """Both the weights and values vectors must be either lists or tuples"""   )

  __magic_name__								=			len(A_   )
  if num_items != len(A_   ):
    __magic_name__								=			(
        """The number of weights must be the same as the number of values.\n"""
        f'''But got {num_items} weights and {len(A_   )} values'''
    )
    raise ValueError(A_   )
  for i in range(A_   ):
    if not isinstance(wt[i],	A_   ):
      __magic_name__								=			(
          """All weights must be integers but got weight of """
          f'''type {type(wt[i]   )} at index {i}'''
      )
      raise TypeError(A_   )

  __magic_name__	,       __magic_name__								=			knapsack(A_,	A_,	A_,	A_   )
  __magic_name__								=			set()
  _construct_solution(A_,	A_,	A_,	A_,	A_   )

  return optimal_val, example_optional_set

def a__       (			A_,	A_,	A_,	A_,	A_   ):






  '''simple docstring'''





  if i > 0 and j > 0:
    if dp[i - 1][j] == dp[i][j]:
      _construct_solution(A_,	A_,	i - 1,	A_,	A_   )
    else:
      optimal_set.add(A_   )
      _construct_solution(A_,	A_,	i - 1,	j - wt[i - 1],	A_   )


if __name__ == "__main__":
    __lowerCAmelCase     :	Union[str, Any]       			=  [3, 2, 4, 4]
    __lowerCAmelCase     :	Dict       			=  [4, 3, 2, 3]
    __lowerCAmelCase     :	Any       			=  4
    __lowerCAmelCase     :	List[str]       			=  6
    __lowerCAmelCase     :	Optional[Any]       			=  [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
    __lowerCAmelCase			, __lowerCAmelCase     :	int       			=  knapsack(w, wt, val, n)
    print(optimal_solution)
    print(mf_knapsack(n, wt, val, w))  # switched the n and w

    # testing the dynamic programming problem with example
    # the optimal subset for the above example are items 3 and 4
    __lowerCAmelCase			, __lowerCAmelCase     :	str       			=  knapsack_with_example_solution(w, wt, val)
    assert optimal_solution == 8
    assert optimal_subset == {3, 4}
    print('optimal_value = ', optimal_solution)
    print('An optimal subset corresponding to the optimal value', optimal_subset)



from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType




class 			UpperCAmelCase_     (					_A	):


  '''simple docstring'''







  a__       			=						["""image_processor""", """tokenizer"""]
  a__       			=						"""BridgeTowerImageProcessor"""
  a__       			=						("""RobertaTokenizer""", """RobertaTokenizerFast""")
  def __init__(					self     :					Optional[Any]     ,				UpperCamelCase__     :					str     ,				UpperCamelCase__     :					Any       )     ->      Optional[int]:







    """simple docstring"""






    super().__init__(UpperCamelCase__     ,				UpperCamelCase__       )
  def __call__(					self     :					Optional[int]     ,				UpperCamelCase__     :					Tuple     ,				UpperCamelCase__     :					Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None     ,				UpperCamelCase__     :					bool = True     ,				UpperCamelCase__     :					Union[bool, str, PaddingStrategy] = False     ,				UpperCamelCase__     :					Union[bool, str, TruncationStrategy] = None     ,				UpperCamelCase__     :					Optional[int] = None     ,				UpperCamelCase__     :					int = 0     ,				UpperCamelCase__     :					Optional[int] = None     ,				UpperCamelCase__     :					Optional[bool] = None     ,				UpperCamelCase__     :					Optional[bool] = None     ,				UpperCamelCase__     :					bool = False     ,				UpperCamelCase__     :					bool = False     ,				UpperCamelCase__     :					bool = False     ,				UpperCamelCase__     :					bool = False     ,				UpperCamelCase__     :					bool = True     ,				UpperCamelCase__     :					Optional[Union[str, TensorType]] = None     ,				**UpperCamelCase__     :					Dict     ,				)     ->      BatchEncoding:







    """simple docstring"""






    __magic_name__								=			self.tokenizer(
        text=UpperCamelCase__     ,				add_special_tokens=UpperCamelCase__     ,				padding=UpperCamelCase__     ,				truncation=UpperCamelCase__     ,				max_length=UpperCamelCase__     ,				stride=UpperCamelCase__     ,				pad_to_multiple_of=UpperCamelCase__     ,				return_token_type_ids=UpperCamelCase__     ,				return_attention_mask=UpperCamelCase__     ,				return_overflowing_tokens=UpperCamelCase__     ,				return_special_tokens_mask=UpperCamelCase__     ,				return_offsets_mapping=UpperCamelCase__     ,				return_length=UpperCamelCase__     ,				verbose=UpperCamelCase__     ,				return_tensors=UpperCamelCase__     ,				**UpperCamelCase__     ,				)
    # add pixel_values + pixel_mask
    __magic_name__								=			self.image_processor(
        UpperCamelCase__     ,				return_tensors=UpperCamelCase__     ,				do_normalize=UpperCamelCase__     ,				do_center_crop=UpperCamelCase__     ,				**UpperCamelCase__       )
    encoding.update(UpperCamelCase__       )

    return encoding
  def 				_lowercase				(					self     :					Optional[Any]     ,				*UpperCamelCase__     :					Optional[Any]     ,				**UpperCamelCase__     :					str       )     ->      str:







    """simple docstring"""






    return self.tokenizer.batch_decode(*UpperCamelCase__     ,				**UpperCamelCase__       )
  def 				_lowercase				(					self     :					Dict     ,				*UpperCamelCase__     :					int     ,				**UpperCamelCase__     :					Optional[Any]       )     ->      str:







    """simple docstring"""






    return self.tokenizer.decode(*UpperCamelCase__     ,				**UpperCamelCase__       )





  @property
  def 				_lowercase				(					self     :					Tuple       )     ->      Union[str, Any]:







    """simple docstring"""






    __magic_name__								=			self.tokenizer.model_input_names
    __magic_name__								=			self.image_processor.model_input_names
    return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names       )       )

